What does the United States government have to do with regular and irregular polygons? A lot, actually! If you look at one of its most famous buildings, you will see a polygon in its design. Yes, the Pentagon is actually a pentagon!

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In 1941, a group of U.S. military officials gathered together as World War II was raging in Europe. They discussed American involvement in the war, but they also talked about the need for a new military headquarters. After a lot of thought about its location, they settled on a 67-acre site within plot of land known as Arlington Farms. The site was an irregular pentagon that was bound on five sides by roads.

In July of that year, George Edwin Bergstrom designed the headquarters, deciding to match its shape to the site's borders. He came up with two irregular pentagon-shaped rings of interlinking buildings, one inside the other. After Congress approved plans to begin construction, President Franklin D. Roosevelt decided to move the building to a different site within the Arlington Farms land. This new site was no longer bound on five sides. However, there wasn't time to change the designs, so the architect continued with the pentagonal plans—though the shape could now be made regular and symmetrical. The total number of rings was brought to five. The building's design is so unique that many people today refer to the U.S. Department of Defense as simply "the Pentagon."